The study of the sensitivity and the specificity of a classification test constitute a powerful kind of analysis since it provides specialists with very detailed information useful for cancer diagnosis. In this work, we propose the use of a multiobjective genetic algorithm for gene selection of Microarray datasets. This algorithm performs gene selection from the point of view of the sensitivity and the specificity, both used as quality indicators of the classification test applied to the previously selected genes. In this algorithm, the classification task is accomplished by Support Vector Machines; in addition a 10-Fold Cross-Validation is applied to the resulting subsets. The emerging behavior of all these techniques used together is noticeable, since this approach is able to offer, in an original and easy way, a wide range of accurate solutions to professionals in this area. The effectiveness of this approach is proved on public cancer datasets by working out new and promising results. A comparative analysis of our approach using two and three objectives, and with other existing algorithms, suggest that our proposal is highly appropriate for solving this problem.